This book presents the proceedings of the international
conference Particle Systems and Partial Differential Equations I,
which took place at the Centre of Mathematics of the University of
Minho, Braga, Portugal, from the 5th to the 7th of December,
2012.
The purpose of the conference was to bring together world
leaders to discuss their topics of expertise and to present some of
their latest research developments in those fields. Among the
participants were researchers in probability, partial differential
equations and kinetics theory. The aim of the meeting was to
present to a varied public the subject of interacting particle
systems, its motivation from the viewpoint of physics and its
relation with partial differential equations or kinetics theory and
to stimulate discussions and possibly new collaborations among
researchers with different backgrounds.
The book contains lecture notes written by Francois Golse on the
derivation of hydrodynamic equations (compressible and
incompressible Euler and Navier-Stokes) from the Boltzmann
equation, and several short papers written by some of the
participants in the conference. Among the topics covered by the
short papers are hydrodynamic limits; fluctuations; phase
transitions; motions of shocks and anti shocks in exclusion
processes; large number asymptotics for systems with
self-consistent coupling; quasi-variational inequalities; unique
continuation properties for PDEs and others.
The book will benefit probabilists, analysts and mathematicians
who are interested in statistical physics, stochastic processes,
partial differential equations and kinetics theory, along with
physicists."
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